Pythagorean Theorem Worksheet. Round Each Number To The Nearest Tenth.

Mathematics

1 answer:

dybincka [34]2 years ago

4 0

Answer:

1. 10

2. 5

3. 10

4. 8

Step-by-step explanation:

1. 8²+6² = 100

The square root of 100 = 10

2. 3²+4² = 25

The square root of 25 = 5

3. 26²-24²=100

The square root of 100 = 10

4. 10²-6² = 64

The square root of 64 = 8

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Find symmetric equations for the line of intersection of the planes. z = 4x − y − 13, z = 6x + 5y − 13

MArishka [77]

The intersection line of two planes is the cross product of the normal vectors of the two planes.

p1: z=4x-y-13 => 4x-y-z=13
p2: z=6x+5y-13 => 6x+5y-z=13
The corresponding normal vectors are:
n1=<4,-1,-1>
n2=<6,5,-1>

The direction vector of the intersection line is the cross product of the two normals,
vl=
i j k
4 -1 -1
6 5 -1
=<1+5, -6+4, 20+6>
=<6,-2,26>
We simplify the vector by reducing its length by half, i.e.
vl=<3,-1,13>

To find the equation of the line, we need to find a point on the intersection line.
Equate z: 4x-y-13=6x+5y-13 => 2x+6y=0 => x+3y=0.
If x=0, then y=0, z=-13 => line passes through (0,0,-13)

Proceed to find the equation of the line:
L: (0,0,-13)+t(3,-1,13)
Convert to symmetric form:
$\frac{x-0}{3}=\frac{y-0}{-1}=\frac{z-(-13)}{13}$
=>
$\frac{x}{3}=\frac{-y}{1}=\frac{z+13}{13}$

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3 years ago

How do you Subtract 9x^2 + 22x - 46 from 12x^2 - 8x + 12.

Luba_88 [7]

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